Statistics for Epidemiology

by Jewell; Nicholas P.

• ISBN13: 9781584884330
• ISBN10: 1584884339
• Format: Hardcover
• Copyright: 2003-08-26
• Publisher: Chapman & Hall/

Summary

Statistical ideas have been integral to the development of epidemiology and continue to provide the tools needed to interpret epidemiological studies. Although epidemiologists do not need a highly mathematical background in statistical theory to conduct and interpret such studies, they do need more than an encyclopedia of "recipes."Statistics for Epidemiology achieves just the right balance between the two approaches, building an intuitive understanding of the methods most important to practitioners and the skills to use them effectively. It develops the techniques for analyzing simple risk factors and disease data, with step-by-step extensions that include the use of binary regression. It covers the logistic regression model in detail and contrasts it with the Cox model for time-to-incidence data. The author uses a few simple case studies to guide readers from elementary analyses to more complex regression modeling. Following these examples through several chapters makes it easy to compare the interpretations that emerge from varying approaches.Written by one of the top biostatisticians in the field, Statistics for Epidemiology stands apart in its focus on interpretation and in the depth of understanding it provides. It lays the groundwork that all public health professionals, epidemiologists, and biostatisticians need to successfully design, conduct, and analyze epidemiological studies.

Author Biography

Nicholas P. Jewell is Professor of Biostatistics and Statistics at the University of California, Berkeley, USA

Table of Contents

1 Introduction	1	(8)
1.1 Disease processes	1	(1)
1.2 Statistical approaches to epidemiological data	2	(3)
1.2.1 Study design	3	(1)
1.2.2 Binary outcome data	4	(1)
1.3 Causality	5	(1)
1.4 Overview	5	(2)
1.4.1 Caution: what is not covered	7	(1)
1.5 Comments and further reading	7	(2)
2 Measures of Disease Occurrence	9	(10)
2.1 Prevalence and incidence	9	(3)
2.2 Disease rates	12	(3)
2.2.1 The hazard function	13	(2)
2.3 Comments and further reading	15	(1)
2.4 Problems	16	(3)
3 The Role of Probability in Observational Studies	19	(12)
3.1 Simple random samples	20	(1)
3.2 Probability and the incidence proportion	21	(1)
3.3 Inference based on an estimated probability	22	(2)
3.4 Conditional probabilities	24	(2)
3.4.1 Independence of two events	26	(1)
3.5 Example of conditional probabilities-Berkson's bias	26	(2)
3.6 Comments and further reading	28	(1)
3.7 Problems	29	(2)
4 Measures of Disease-Exposure Association	31	(12)
4.1 Relative risk	31	(1)
4.2 Odds ratio	32	(1)
4.3 The odds ratio as an approximation to the relative risk	33	(1)
4.4 Symmetry of roles of disease and exposure in the odds ratio	34	(1)
4.5 Relative hazard	35	(2)
4.6 Excess risk	37	(1)
4.7 Attributable risk	38	(2)
4.8 Comments and further reading	40	(1)
4.9 Problems	41	(2)
5 Study Designs	43	(16)
5.1 Population-based studies	45	(2)
5.1.1 Example-mother's marital status and infant birthweight	46	(1)
5.2 Exposure-based sampling-cohort studies	47	(1)
5.3 Disease-based sampling-case-control studies	48	(2)
5.4 Key variants of the case-control design	50	(5)
5.4.1 Risk-set sampling of controls	51	(2)
5.4.2 Case-cohort studies	53	(2)
5.5 Comments and further reading	55	(1)
5.6 Problems	56	(3)
6 Assessing Significance in a 2 x 2 Table	59	(14)
6.1 Population-based designs	59	(3)
6.1.1 Role of hypothesis tests and interpretation of p-values	61	(1)
6.2 Cohort designs	62	(2)
6.3 Case-control designs	64	(4)
6.3.1 Comparison of the study designs	65	(3)
6.4 Comments and further reading	68	(3)
6.4.1 Alternative formulations of the 2 test statistic	69	(1)
6.4.2 When is the sample size too small to do a x2 test?	70	(1)
6.5 Problems	71	(2)
7 Estimation and Inference for Measures of Association	73	(20)
7.1 The odds ratio	73	(8)
7.1.1 Sampling distribution of the odds ratio	74	(3)
7.1.2 Confidence interval for the odds ratio	77	(1)
7.1.3 Example-coffee drinking and pancreatic cancer	78	(1)
7.1.4 Small sample adjustments for estimators of the odds ratio	79	(2)
7.2 The relative risk	81	(2)
7.2.1 Example-coronary heart disease in the Western Collaborative Group Study	82	(1)
7.3 The excess risk	83	(1)
7.4 The attributable risk	84	(1)
7.5 Comments and further reading	85	(5)
7.5.1 Measurement error or misclassification	86	(4)
7.6 Problems	90	(3)
8 Causal Inference and Extraneous Factors: Confounding and Interaction	93	(30)
8.1 Causal inference	94	(8)
8.1.1 Counterfactuals	94	(5)
8.1.2 Confounding variables	99	(1)
8.1.3 Control of confounding by stratification	100	(2)
8.2 Causal graphs	102	(7)
8.2.1 Assumptions in causal graphs	105	(1)
8.2.2 Causal graph associating childhood vaccination to subsequent health condition	106	(1)
8.2.3 Using causal graphs to infer the presence of confounding	107	(2)
8.3 Controlling confounding in causal graphs	109	(3)
8.3.1 Danger: controlling for colliders	109	(2)
8.3.2 Simple rules for using a causal graph to choose the crucial confounders	111	(1)
8.4 Collapsibility over strata	112	(4)
8.5 Comments and further reading	116	(3)
8.6 Problems	119	(4)
9 Control of Extraneous Factors	123	(24)
9.1 Summary test of association in a series of 2 x 2 tables	123	(5)
9.1.1 The Cochran-Mantel-Haenszel test	125	(3)
9.1.2 Sample size issues and a historical note	128	(1)
9.2 Summary estimates and confidence intervals for the odds ratio, adjusting for confounding factors	128	(6)
9.2.1 Woolfs method on the logarithm scale	129	(1)
9.2.2 The Mantel-Haenszel method	130	(1)
9.2.3 Example-the Western Collaborative Group Study: part 2	131	(2)
9.2.4 Example-coffee drinking and pancreatic cancer: part 2	133	(1)
9.3 Summary estimates and confidence intervals for the relative risk, adjusting for confounding factors	134	(2)
9.3.1 Example-the Western Collaborative Group Study: part 3	135	(1)
9.4 Summary estimates and confidence intervals for the excess risk, adjusting for confounding factors	136	(2)
9.4.1 Example-the Western Collaborative Group Study: part 4	137	(1)
9.5 Further discussion of confounding	138	(5)
9.5.1 How do adjustments for confounding affect precision?	138	(4)
9.5.2 An empirical approach to confounding	142	(1)
9.6 Comments and further reading	143	(1)
9.7 Problems	144	(3)
10 Interaction	147	(18)
10.1 Multiplicative and additive interaction	148	(2)
10.1.1 Multiplicative interaction	148	(1)
10.1.2 Additive interaction	149	(1)
10.2 Interaction and counterfactuals	150	(2)
10.3 Test of consistency of association across strata	152	(8)
10.3.1 The Woolf method	153	(2)
10.3.2 Alternative tests of homogeneity	155	(1)
10.3.3 Example-the Western Collaborative Group Study: part 5	156	(2)
10.3.4 The power of the test for homogeneity	158	(2)
10.4 Example of extreme interaction	160	(1)
10.5 Comments and further reading	161	(1)
10.6 Problems	162	(3)
11 Exposures at Several Discrete Levels	165	(14)
11.1 Overall test of association	165	(2)
11.2 Example-coffee drinking and pancreatic cancer: part 3	167	(1)
11.3 A test for trend in risk	167	(4)
11.3.1 Qualitatively ordered exposure variables	169	(1)
11.3.2 Goodness of fit and nonlinear trends in risk	170	(1)
11.4 Example-the Western Collaborative Group Study: part 6	171	(2)
11.5 Example-coffee drinking and pancreatic cancer: part 4	173	(2)
11.6 Adjustment for confounding, exact tests, and interaction	175	(1)
11.7 Comments and further reading	176	(1)
11.8 Problems	176	(3)
12 Regression Models Relating Exposure to Disease	179	(20)
12.1 Some introductory regression models	181	(2)
12.1.1 The linear model	181	(2)
12.1.2 Pros and cons of the linear model	183	(1)
12.2 The log linear model	183	(1)
12.3 The probit model	184	(2)
12.4 The simple logistic regression model	186	(2)
12.4.1 Interpretation of logistic regression parameters	187	(1)
12.5 Simple examples of the models with a binary exposure	188	(2)
12.6 Multiple logistic regression model	190	(6)
12.6.1 The use of indicator variables for discrete exposures	191	(5)
12.7 Comments and further reading	196	(1)
12.8 Problems	196	(3)
13 Estimation of Logistic Regression Model Parameters	199	(22)
13.1 The likelihood function	199	(8)
13.1.1 The likelihood function based on a logistic regression model	201	(3)
13.1.2 Properties of the log likelihood function and the maximum likelihood estimate	204	(2)
13.1.3 Null hypotheses that specify more than one regression coefficient	206	(1)
13.2 Example-the Western Collaborative Group Study: part 7	207	(5)
13.3 Logistic regression with case-control data	212	(3)
13.4 Example-coffee drinking and pancreatic cancer: part 5	215	(3)
13.5 Comments and further reading	218	(1)
13.6 Problems	219	(2)
14 Confounding and Interaction within Logistic Regression Models	221	(22)
14.1 Assessment of confounding using logistic regression models	221	(4)
14.1.1 Example-the Western Collaborative Group Study: part 8	223	(2)
14.2 Introducing interaction into the multiple logistic regression model	225	(2)
14.3 Example-coffee drinking and pancreatic cancer: part 6	227	(3)
14.4 Example-the Western Collaborative Group Study: part 9	230	(1)
14.5 Collinearity and centering variables	230	(5)
14.5.1 Centering independent variables	233	(1)
14.5.2 Fitting quadratic models	233	(2)
14.6 Restrictions on effective use of maximum likelihood techniques	235	(1)
14.7 Comments and further reading	236	(4)
14.7.1 Measurement error	237	(1)
14.7.2 Missing data	237	(3)
14.8 Problems	240	(3)
15 Goodness of Fit Tests for Logistic Regression Models and Model Building	243	(14)
15.1 Choosing the scale of an exposure variable	243	(3)
15.1.1 Using ordered categories to select exposure scale	244	(1)
15.1.2 Alternative strategies	245	(1)
15.2 Model building	246	(4)
15.3 Goodness of fit	250	(4)
15.3.1 The Hosmer-Lemeshow test	252	(2)
15.4 Comments and further reading	254	(1)
15.5 Problems	255	(2)
16 Matched Studies	257	(28)
16.1 Frequency matching	257	(1)
16.2 Pair matching	258	(6)
16.2.1 Mantel-Haenszel techniques applied to pair-matched data	262	(2)
16.2.2 Small sample adjustment for odds ratio estimator	264	(1)
16.3 Example-pregnancy and spontaneous abortion in relation to coronary heart disease in women	264	(1)
16.4 Confounding and interaction effects	265	(4)
16.4.1 Assessing interaction effects of matching variables	265	(1)
16.4.2 Possible confounding and interactive effects due to nonmatching variables	266	(3)
16.5 The logistic regression model for matched data	269	(5)
16.5.1 Example-pregnancy and spontaneous abortion in relation to coronary heart disease in women: part 2	271	(3)
16.6 Example-the effect of birth order on respiratory distress syndrome in twins	274	(2)
16.7 Comments and further reading	276	(3)
16.7.1 When can we break the match?	277	(1)
16.7.2 Final thoughts on matching	278	(1)
16.8 Problems	279	(6)
17 Alternatives and Extensions to the Logistic Regression Model	285	(16)
17.1 Flexible regression model	285	(4)
17.2 Beyond binary outcomes and independent observations	289	(1)
17.3 Introducing general risk factors into formulation of the relative hazard-the Cox model	290	(3)
17.4 Fitting the Cox regression model	293	(2)
17.5 When does time at risk confound an exposure-disease relationship?	295	(2)
17.5.1 Time-dependent exposures	296	(1)
17.5.2 Differential loss to follow-up	296	(1)
17.6 Comments and further reading	297	(1)
17.7 Problems	298	(3)
18 Epilogue: The Examples	301	(2)
References	303	(8)
Glossary of Common Terms and Abbreviations	311	(8)
Index	319